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Simplifying -36x2 + 144x + -48 = 0 Reorder the terms: -48 + 144x + -36x2 = 0 Solving -48 + 144x + -36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-4 + 12x + -3x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-4 + 12x + -3x2)' equal to zero and attempt to solve: Simplifying -4 + 12x + -3x2 = 0 Solving -4 + 12x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.333333333 + -4x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -4x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -4x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -4x + x2 = 0 + -1.333333333 -4x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -4x + x2 = -1.333333333 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.333333333 + 4 Reorder the terms: 4 + -4x + x2 = -1.333333333 + 4 Combine like terms: -1.333333333 + 4 = 2.666666667 4 + -4x + x2 = 2.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.666666667 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (x + -2) equal to 1.632993162 and -1.632993162.Subproblem 1
x + -2 = 1.632993162 Simplifying x + -2 = 1.632993162 Reorder the terms: -2 + x = 1.632993162 Solving -2 + x = 1.632993162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.632993162 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.632993162 + 2 x = 1.632993162 + 2 Combine like terms: 1.632993162 + 2 = 3.632993162 x = 3.632993162 Simplifying x = 3.632993162Subproblem 2
x + -2 = -1.632993162 Simplifying x + -2 = -1.632993162 Reorder the terms: -2 + x = -1.632993162 Solving -2 + x = -1.632993162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.632993162 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.632993162 + 2 x = -1.632993162 + 2 Combine like terms: -1.632993162 + 2 = 0.367006838 x = 0.367006838 Simplifying x = 0.367006838Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.632993162, 0.367006838}Solution
x = {3.632993162, 0.367006838}
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